Fuming Jiang

Elasticity of hydrous wadsleyite to 12 GPa: Implications for Earth's transition zone

Knowledge of the pressure effect on elasticity of hydrous olivine polymorphs is necessary to model seismic wave speeds for potential hydrous regions of the mantle. Here we report single-crystal elastic properties of wadsleyite, {beta}-Mg2SiO4, with 0.84 wt.% H2O measured to 12 GPa by Brillouin scattering. Pressure derivatives of the aggregate bulk modulus, K{prime} S0, and shear modulus, G{prime}0, of hydrous wadsleyite are 4.1(1) and 1.4(1) respectively. These values are indistinguishable within uncertainty from those of anhydrous wadsleyite. We estimate that {approx}1 wt.% H2O in wadsleyite at 410-km depth can reconcile seismic bulk sound velocities with a pyrolite-composition mantle by using our measured high-pressure elastic constants. If the H2O content of the mantle is much less than 1 wt.%, then other factors need to be considered to explain the velocity contrast of the 410-km discontinuity. Variations in water content with depth may also contribute to the anomalously steep seismic velocity gradient in the mantle transition zone.

Single-crystal elasticity of brucite, Mg(OH)2, to 15 GPa by Brillouin scattering

Abstract The second-order elastic constants of brucite were determined by Brillouin scattering to 15 GPa in a diamond anvil cell. The experiments were carried out using a 4:1 methanol-ethanol mixture as pressure medium, and ruby as a pressure standard. Two planes, one perpendicular to the c axis (basal plane) and the other containing the c axis (meridian plane), were measured at room pressure and 10 elevated pressures. Individual elastic stiffnesses, aggregate moduli, and their pressure derivatives were obtained by fitting the data to Eulerian finite strain equations. The inversion yields individual elastic constants of C11 = 154.0(14) GPa, C33 = 49.7(7) GPa, C12 = 42.1(17) GPa, C13 = 7.8(25) GPa, C14 = 1.3(10) GPa, C44 = 21.3(4) GPa, and their pressure derivatives of (∂C11/∂P)0 = 9.0(2), (∂C33/∂P)0 = 14.0(5), (∂C12/∂P)0 = 3.2(2), (∂C13/∂P)0 = 5.0(1), (∂C14/∂P)0 = 0.9(1), (∂C44/∂P)0 = 3.9(1). Aggregate moduli and their pressure derivatives are KS0 = 36.4(9) GPa, G0 = 31.3(2) GPa, (∂KS/∂P)T0 = 8.9(4), (∂G/∂P)0 = 4.3(1) for the Reuss bound, and KS0 = 43.8(8) GPa, G0 = 35.2(3) GPa, (∂KS/∂P)T0 = 6.8(2), (∂G/P)0 = 3.4(1) for the Voigt-Reuss-Hill average. The ratio of the linear compressibility along the c and a axes decreased from 4.7 to 1.3 over the examined pressure range. The shear anisotropy (C66/C44) decreased from 2.6(1) at ambient condition to 1.3(1) with increase of pressure to 12 GPa. Axial compressibilities and a compression curve constructed from our Brillouin data are in good agreement with previous X-ray diffraction data. The increased interlayer interactions and hydrogen repulsion that occurs as brucite is compressed produce a continuous variation of elastic properties rather than any abrupt discontinuities.

Single-crystal elasticity of zoisite Ca2Al3Si3O12 (OH) by Brillouin scattering

Abstract The single-crystal elastic constants of zoisite Ca2Al3Si3O12(OH) were determined by Brillouin scattering at ambient conditions. The elastic tensor was obtained by an inversion of acoustic velocity data for three different crystal planes. The aggregate bulk modulus, shear modulus, and Poisson.s ratio are KS0 = 125.3(4) GPa, G0 = 72.9(2) GPa, and σ0 = 0.26(1) for the VRH (Voigt-Reuss-Hill) average, respectively. The maximum azimuthal anisotropy of zoisite is 22% for compressional velocity and 33% for shear velocity. The maximum shear splitting is 21% along the [001] direction. Our results resolve the discrepancies in bulk modulus and axial compressibilities reported from static compression studies, and provide the first experimental constraints on the shear modulus. Trends in the elastic moduli of minerals in the CaO-Al2O3-SiO2-H2O (CASH) system are evaluated.

Single-crystal elasticity of andradite garnet to 11 GPa

The high-pressure elastic properties of single-crystal andradite garnet Ca3Fe 3+ Si3O12 were determined by Brillouin scattering to 11 GPa. The pressure dependence of the elastic stiffness constants and aggregate bulk and shear moduli were obtained by inversion of the data to finite Eulerian strain equations. The inversion yieldsC11 = 286.7 ±0. 6G Pa,C12 = 88.6 ±0. 6G Pa, C44 = 83.8 ± 0. 3G Pa,K0S = 154.5 ± 0. 6G Pa,G0S = 89.7 ± 0. 4G Pa, (∂K0T /∂P)T = 4.71 ± 0.1, and (∂G0/∂P)T = 1.25 ± 0.05. Both individual and aggregate elastic moduli define nearly linear modulus–pressure trends. The elastic anisotropy of andradite garnet si ncr eases weakly in magnitude with compression. Previous studies of the high-pressure elasticity of andradite garnet are highly discrepant, with reported pressure derivatives of the bulk modulus varying by 46% and pressure derivatives of the shear modulus varying by 253%. We are able to provide plausible explanations for these discrepancies. In particular, differences between previous x-ray diffraction data and a static compression curve constructed from our Brillouin data can be attributed to the effects of non-hydrostatic stresses on the x-ray data.

Correction to “Effects of hydration on the elastic properties of olivine”

[1] In the paper ‘‘Effects of hydration on the elastic properties of olivine’’ by S. D. Jacobsen et al. (Geophysical Research Letters, 35, L14303, doi:10.1029/2008GL034398, 2008), the sample of hydrous olivine labeled hy-Fo97 with (001) orientation in the bottom plot of original Figure 1b has been subsequently identified by Raman spectroscopy as OH-chondrodite, (Mg,Fe)5Si2O8(OH)2 [e.g., Lin et al., 1999]. The OH-chondrodite co-existed with hydrous forsterite in the synthesis run, and all other samples in the study have been confirmed to be hydrous forsterite. Upon removing the OH-chondrodite platelet from the fit, we obtain a corrected set of elastic constants (Cij) and crystallographic orientations for hy-Fo97 using a two-plane fit, displayed in corrected Figure 1 and presented in corrected Table 1. The original Table 2 of anisotropy factors has been updated and presented here in corrected Table 2. Brillouin spectra from the two remaining orientations of hy-Fo97 determine eight of the nine Cij, leaving C12 unconstrained. As a result, C12 was fixed to the value obtained for hy-Fo100 and a large uncertainty of ±5 GPa in this parameter was assumed in calculating the aggregate bulk (KS0) and shear (G) moduli. [2] In addition, a minor correction to the elastic constants of hydrous forsterite (hy-Fo100) is presented in revised Table 1 because the original calculation used an earlier estimated density of 3.19 g/cm, instead of the actual measured X-ray density of 3.180(3) g/cm. The measured X-ray density of 3.180(3) g/cm was correctly reported in the original text, but not used in the calculation of Cij. The revised Cij of hydrous forsterite are affected by only 0.2–0.3% from the original calculation as a result of the error. [3] The revised values of elastic properties for hy-Fo100 and hy-Fo97 presented in the corrected Table 1 apply to the following statements in the text: [4] The last four sentences of paragraph [1] should read: The adiabatic bulk (KS0) and shear (G0) moduli of hy-Fo100 are 125.4(±0.2) GPa and 79.6(±0.1) GPa, respectively. For hy-Fo97, we obtain KS0 = 125.2(±0.8) GPa and G0 = 77.7(±0.3) GPa. Compared with anhydrous forsterite, the combined effects of 3 mol% Fe and 0.8 wt% H2O reduce bulk and shear moduli by 2.9(±0.6)% and 4.5(±0.4)% respectively, with greater reductions expected for more iron-rich Fo90 mantle compositions. Although lattice preferred orientation (LPO) studies have not been carried out under relevant conditions of water or pressure, analysis of idealized single-crystal anisotropy for various known LPO types predicts no more than 2% effect of hydration on Swave splitting anisotropy in olivine. [5] The last sentence of paragraph [9] should read: We measured two platelets of hy-Fo97 with fitted orientations of (100) and (010), shown in the corrected Figure 1b. [6] The last two sentences of paragraph [10] should read: The addition of 0.89 wt% H2O to forsterite in our hy-Fo100 samples shows a reduction of all Cij by 1.8–4.3%, except C33, which is reduced by only 0.8%. For hy-Fo100, we obtain KS0 = 125.4(±0.2) GPa and G0 = 79.6(±0.1) GPa, which are about 2.7% and 2.2% lower than anhydrous forsterite, respectively. [7] The first two sentences of paragraph [11] should read: Comparing the Cij of hy-Fo97 with anhydrous Fo100 to ascertain the net effect of iron and hydration shows that there is a large reduction in Cij by 2.4–6.4%, except for C23, which increased by 2.1%. For hy-Fo97, we obtain KS0 = 125.2(±0.8) GPa and G0 = 77.7(±0.3) GPa, which are 2.9% and 4.5% lower than anhydrous forsterite. [8] The last sentence of paragraph [11] should read: The aggregate hy-Fo97 velocities Vp and Vs (with only 3 mol% Fe) are 2.1% and 2.4% lower, respectively, than anhydrous forsterite, suggesting that hydrous Fo90 olivine, closer to mantle composition, would exhibit even further reduced velocities.

Compositional dependence of the elastic wave velocities of mantle minerals : Implications for seismic properties of mantle rocks

Using single-crystal elasticity data we constrain the effect of chemical substitutions on the elastic properties of mantle minerals and estimate the consequences for the seismic properties of mantle rocks. At ambient conditions the calculated relative variation of compressional and shear velocities ∂lnv P /∂X Fe and ∂Inv S /∂X Fe due to Fe-Mg substitution, range between -0.05 and -0.46 and between -0.08 and -0.74 respectively in the main mantle minerals. The corresponding heterogeneity ratios R = ∂lnv S /∂lnv P for Fe-Mg substitution range between 0.9 and 1.7 suggesting that the effect of this substitution is very different in different solid solutions systems. More limited experimental results for Ca-Mg substitution and Al enrichment in pyroxenes and garnets were also evaluated. Only Ca-Mg substitution in garnets is found to produce large (>2.0) values of R. Heterogeneity parameters at upper mantle and transition zone conditions can be substantially different from ambient P-T values in some cases. Using a first-order approximation of the effect of Fe-Mg substitution on the elastic properties of the most relevant upper mantle rocks, we find that the sensitivities of seismic velocities to Fe enrichment can vary as much as 2-3 times between the different rock types. We estimate that in the upper mantle the value of ∂lnv S /∂lnv P for pyrolite, piclogite and harzburgite decreases from 1.5 to 1.0 at the base of the transition zone, while it only decreases from 1.5 to 1.3 in mid ocean ridge basalt eclogite, which is enriched in garnet. We also estimate that the seismic effect of lateral changes in lithology from average mantle to subducted slab rocks decreases in intensity at upper mantle and transition zone depths, in agreement with seismic tomographic models. Information about the effects of Ca and Al enrichment are still too incomplete to make predictions of their effects on whole rocks, but they could be relevant based on our limited information.